“New viewers are finding these shows on a digital service, catching up on prior seasons and then tuning into AMC for new seasons in greater numbers, many for the first time,” Mr. Sapan said on a conference call with analysts Thursday.

Last Friday, AMC disclosed that Dish Network was planning to drop all four of AMC’s channels, including AMC itself, WE tv, the Sundance Channel and IFC, from the end of June. Dish confirmed the decision, citing the high cost of the channels in comparison with their viewership.

Dish Chairman Charlie Ergen said on Monday that the availability of AMC’s hit shows such as “Mad Men” and “Breaking Bad” on online video outlets had “devalued their programming content” and contributed to Dish’s decision not to renew the channels.

AMC warned that its future financial performance could be affected if its channels were dropped by Dish, but it didn’t specify by how much. Dish has more than 14 million subscribers.

Mr. Sapan said that AMC’s networks remains “underpriced” in the market, though it reported an 8% increase in affiliate fees from distributors in the first quarter. Mr. Sapan said the pickup was “the beginning of an upward trend in more recent agreements” with distributors.

However, he continued to attribute Dish’s decision to bad blood in a years-old lawsuit between the two companies. Dish is “trying to create leverage for itself” in the case, Mr. Sapan said. Dish has said that the lawsuit and its decision to drop AMC are two separate matters.

AMC Networks, which was spun off from Cablevision Systems Corp. last June, has reinvented itself in recent years with a slate of highly rated original-show successes, shedding its image as a sleepy broadcaster of independent movies and classic westerns. The transformation has come at a cost, however, as higher programming and marketing expenses to promote shows like “Mad Men” cut into its bottom line.

AMC Networks reported a profit of $43.2 million, or 60 cents a share, up from $29.8 million, or 43 cents, a year earlier. Revenue jumped 20% to $326.2 million as the namesake channel contributed to a 30% rise in advertising revenue.

Operating margin rose to 29.7% from 25.9%.

National-networks revenue rose 21% to $304.2 million on stronger affiliate fees. Revenue from its international-and-other segment—which includes its international programming, independent film distribution and network technical-services businesses—grew 3.8% to $26.3 million.